Playing Logic Programs with the Alpha-Beta Algorithm
Alpha-Beta is a well known optimized algorithm used to compute the values of classical combinatorial games, like chess and checkers The known proofs of correctness of Alpha-Beta do rely on very specific properties of the values used in the classical context (integers or reals), and on the finiteness of the game tree. In this paper we prove that Alpha-Beta correctly computes the value of a game tree even when these values are chosen in a much wider set of partially ordered domains, which can be pretty far apart from integer and reals, like in the case of the lattice of idempotent substitutions or ex-equations used in logic programming. We do so in a more general setting that allows us to deal with infinite games, and we actually prove that for potentially infinite games Alpha-Beta correctly computes the value of the game whenever it terminates. This correctness proofs allows us to apply Alpha-Beta to new domains, like constraint logic programming.
Unable to display preview. Download preview PDF.
- 4.P. Curien and H. Herbelin. Computing with abstract bohm trees. 1996. 207Google Scholar
- 5.R. Di Cosmo, J.-V. Loddo, and S. Nicolet. A game semantics foundation for logic programming. In C. Palamidessi, H. Glaser, and K. Meinke, editors, PLILP’98, volume 1490 of Lecture Notes in Computer Science, pages 355–373, 1998. 208, 217, 217, 220Google Scholar
- 6.G. Diderich. A survey on minimax trees and associated algorithms. Minimax and its Applications, Kluwer Academic Publishers, 1995. 208Google Scholar
- 9.A. Joyal. Free lattices, communication and money games. Proceedings of the 10th International Congress of Logic, Methodology, and Philosophy of Science, 1995. 207Google Scholar
- 11.F. Lamarche. Game semantics for full propositional linear logic. Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science, pages 464–473, 1995. 207Google Scholar
- 12.G. Owen. Game Theory. W.B. Saunders, 1968. 209Google Scholar
- 13.V. D. P. Baillot and T. Ehrhard. Believe it or not, AJM’s games model is a model of classical linear logic. Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, pages pages 68–75, 1997. 207Google Scholar
- 14.J. Pearl. Heuristics. Intelligent Search Strategies for Computer Problem Solving. Addison Wesley, 1984. 208, 210, 215Google Scholar
- 15.A. Plaat. Research Re: search & Re-search. PhD thesis, Tinbergen Institute and Department of Computer Science, Erasmus University Rotterdam, 1996. 208Google Scholar
- 16.J. von Neumann. Zur Theorie der Gesellschaftsspiele. Mathaematische Annalen, (100):195–320, 1928. 208Google Scholar